Control method for a scanning exposure apparatus

ABSTRACT

A method for controlling a scanning exposure apparatus configured for scanning an illumination profile over a substrate to form functional areas thereon. The method includes determining a control profile for dynamic control of the illumination profile during exposure of an exposure field including the functional areas, in a scanning exposure operation; and optimizing a quality of exposure of one or more individual functional areas. The optimizing may include a) extending the control profile beyond the extent of the exposure field in the scanning direction; and/or b) applying a deconvolution scheme to the control profile, wherein the structure of the deconvolution scheme is based on a dimension of the illumination profile in the scanning direction.

BACKGROUND Cross Reference to Related Applications

This application claims priority of EP application 18164962.5 which wasfiled on Mar. 29, 2018 and NL application 2021296 which was filed onJul. 12, 2018 which are incorporated herein in its entirety byreference.

FIELD OF THE INVENTION

The present invention relates to methods and apparatus for applyingpatterns to a substrate in a lithographic process and/or measuring saidpatterns.

BACKGROUND

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In that instance, a patterning device, whichis alternatively referred to as a mask or a reticle, may be used togenerate a circuit pattern to be formed on an individual layer of theIC. This pattern can be transferred onto a target portion (e.g.comprising part of, one, or several dies) on a substrate (e.g. a siliconwafer). Transfer of the pattern is typically via imaging onto a layer ofradiation-sensitive material (resist) provided on the substrate. Ingeneral, a single substrate will contain a network of adjacent targetportions that are successively patterned. Known lithographic apparatusinclude so-called steppers, in which each target portion is irradiatedby exposing an entire pattern onto the target portion at one time, andso-called scanners, in which each target portion is irradiated byscanning the pattern through a radiation beam in a given direction (the“scanning”-direction) while synchronously scanning the substrateparallel or anti-parallel to this direction. It is also possible totransfer the pattern from the patterning device to the substrate byimprinting the pattern onto the substrate.

In order to monitor the lithographic process, parameters of thepatterned substrate are measured. Parameters may include, for example,the overlay error between successive layers formed in or on thepatterned substrate and critical linewidth (CD) of developedphotosensitive resist. This measurement may be performed on a productsubstrate and/or on a dedicated metrology target. There are varioustechniques for making measurements of the microscopic structures formedin lithographic processes, including the use of scanning electronmicroscopes and various specialized tools. A fast and non-invasive formof specialized inspection tool is a scatterometer in which a beam ofradiation is directed onto a target on the surface of the substrate andproperties of the scattered or reflected beam are measured. Two maintypes of scatterometer are known. Spectroscopic scatterometers direct abroadband radiation beam onto the substrate and measure the spectrum(intensity as a function of wavelength) of the radiation scattered intoa particular narrow angular range. Angularly resolved scatterometers usea monochromatic radiation beam and measure the intensity of thescattered radiation as a function of angle.

Examples of known scatterometers include angle-resolved scatterometersof the type described in US2006033921A1 and US2010201963A1. The targetsused by such scatterometers are relatively large, e.g., 40 μm by 40 μm,gratings and the measurement beam generates a spot that is smaller thanthe grating (i.e., the grating is underfilled). In addition tomeasurement of feature shapes by reconstruction, diffraction basedoverlay can be measured using such apparatus, as described in publishedpatent application US2006066855A1. Diffraction-based overlay metrologyusing dark-field imaging of the diffraction orders enables overlaymeasurements on smaller targets. Examples of dark field imagingmetrology can be found in international patent applications WO2009/078708 and WO 2009/106279 which documents are hereby incorporatedby reference in their entirety. Further developments of the techniquehave been described in published patent publications US20110027704A,US20110043791A, US2011102753A1, US20120044470A, US20120123581A,US20130258310A, US20130271740A and WO2013178422A1. These targets can besmaller than the illumination spot and may be surrounded by productstructures on a wafer. Multiple gratings can be measured in one image,using a composite grating target. The contents of all these applicationsare also incorporated herein by reference.

In performing lithographic processes, such as application of a patternon a substrate or measurement of such a pattern, process control methodsare used to monitor and control the process. Such process controltechniques are typically performed to obtain corrections foracross-substrate (inter-field) and within field (intra-field) processfingerprints. It would be desirable to improve such process controlmethods.

Furthermore, in general terms, a lithographic stage or servo positioningperformance is expressed as a time Moving Average error (MA error) and atime Moving Standard Deviation (MSD) of the error. A critical timewindow here is the time interval that each point on a die is exposed (inother words: receives photons). If the average position error for apoint on the die during this time interval is high (in other words: highMA-error), the effect is a shift of the exposed image, resulting inoverlay errors. If the standard deviation of the position error duringthis time interval is high (in other words: high MSD error), the imagemay smear, resulting in fading errors. It would be desirable to reduceMSD and/or MA errors.

SUMMARY OF THE INVENTION

In a first aspect of the invention, there is provided a method forcontrolling a scanning exposure apparatus configured for scanning anillumination profile over a substrate to form functional areas thereon,the method comprising: obtaining a control profile for dynamic controlof the illumination profile during exposure of an exposure fieldcomprising the functional areas; and configuring the control profile toimprove a quality of exposure of one or more individual functional areasby: a) extending the control profile beyond the extent of the exposurefield in the scanning direction and/or b) applying a deconvolutionscheme to the control profile, wherein the structure of thedeconvolution scheme is based on a dimension of the illumination profilein the scanning direction.

In a second aspect of the invention, there is provided a scanningexposure apparatus comprising a processor operable to perform the methodof any of the first aspect.

In a third aspect of the invention, there is provided a computer programcomprising program instructions operable to perform the method of thesecond aspect when run on a suitable apparatus.

In a fourth aspect of the invention there is provided a method fordetermining a control profile for a scanning exposure apparatusconfigured to scan an illumination profile over a substrate to form anexposure field comprising functional areas thereon, the methodcomprising a step of determining a control profile for dynamic controlof the illumination profile based on improving a quality of exposure ofone or more individual functional areas by: a) allowing the controlprofile to extend beyond the exposure field and/or b) taking thedimension of the illumination profile in the scanning direction intoaccount.

In a fifth aspect of the invention there is provided a method forcontrolling a scanning apparatus configured for scanning a beam ofphotons or particles across a substrate to form functional devicesthereon, the method comprising: obtaining a control profile for dynamiccontrol of the beam during scanning operation, wherein the beam ischaracterized by a beam profile comprising information of a spatialextension of the beam in at least a scanning direction; and optimizing aquality of beam control by applying a deconvolution scheme to thecontrol profile, wherein the structure of the deconvolution scheme isbased on the beam profile.

Further aspects, features and advantages of the invention, as well asthe structure and operation of various embodiments of the invention, aredescribed in detail below with reference to the accompanying drawings.It is noted that the invention is not limited to the specificembodiments described herein. Such embodiments are presented herein forillustrative purposes only. Additional embodiments will be apparent topersons skilled in the relevant art(s) based on the teachings containedherein.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of example,with reference to the accompanying drawings in which:

FIG. 1 depicts a lithographic apparatus together with other apparatusesforming a production facility for semiconductor devices;

FIG. 2 is a flow diagram illustrating a method of control of alithographic process using separation between intra die, intra reticleand inter field fingerprints and an extended control profile beyond thefield limits

FIG. 3 is a graph of an overlay metric dy against field position Y,showing a correction profile for a saw-tooth pattern, the effect of slitconvolution on the correction profile, and the effect of performing afurther slit deconvolution in accordance with an embodiment of theinvention;

FIG. 4 is a flow diagram illustrating the problem of convolution of thecorrection profile with the intensity profile within the exposure slit;and

FIG. 5 is a flow diagram illustrating a method of deconvolution of theexposure slit intensity profile from the correction profile using aWeiner filter, in accordance with an embodiment of the invention.

DETAILED DESCRIPTION

Before describing embodiments of the invention in detail, it isinstructive to present an example environment in which embodiments ofthe present invention may be implemented.

FIG. 1 at 100 shows a lithographic apparatus LA as part of an industrialproduction facility implementing a high-volume, lithographicmanufacturing process. In the present example, the manufacturing processis adapted for the manufacture of for semiconductor products (integratedcircuits) on substrates such as semiconductor wafers. The skilled personwill appreciate that a wide variety of products can be manufactured byprocessing different types of substrates in variants of this process.The production of semiconductor products is used purely as an examplewhich has great commercial significance today.

Within the lithographic apparatus (or “litho tool” 100 for short), ameasurement station MEA is shown at 102 and an exposure station EXP isshown at 104. A control unit LACU is shown at 106. In this example, eachsubstrate visits the measurement station and the exposure station tohave a pattern applied. In an optical lithographic apparatus, forexample, a projection system is used to transfer a product pattern froma patterning device MA onto the substrate using conditioned radiationand a projection system. This is done by forming an image of the patternin a layer of radiation-sensitive resist material.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. The patterning MA device maybe a mask or reticle, which imparts a pattern to a radiation beamtransmitted or reflected by the patterning device. Well-known modes ofoperation include a stepping mode and a scanning mode. As is well known,the projection system may cooperate with support and positioning systemsfor the substrate and the patterning device in a variety of ways toapply a desired pattern to many target portions across a substrate.Programmable patterning devices may be used instead of reticles having afixed pattern. The radiation for example may include electromagneticradiation in the deep ultraviolet (DUV) or extreme ultraviolet (EUV)wavebands. The present disclosure is also applicable to other types oflithographic process, for example imprint lithography and direct writinglithography, for example by electron beam.

The lithographic apparatus control unit LACU which controls all themovements and measurements of various actuators and sensors to receivesubstrates W and reticles MA and to implement the patterning operations.LACU also includes signal processing and data processing capacity toimplement desired calculations relevant to the operation of theapparatus. In practice, control unit LACU will be realized as a systemof many sub-units, each handling the real-time data acquisition,processing and control of a subsystem or component within the apparatus.

Before the pattern is applied to a substrate at the exposure stationEXP, the substrate is processed in at the measurement station MEA sothat various preparatory steps may be carried out. The preparatory stepsmay include mapping the surface height of the substrate using a levelsensor and measuring the position of alignment marks on the substrateusing an alignment sensor. The alignment marks are arranged nominally ina regular grid pattern. However, due to inaccuracies in creating themarks and also due to deformations of the substrate that occurthroughout its processing, the marks deviate from the ideal grid.Consequently, in addition to measuring position and orientation of thesubstrate, the alignment sensor in practice must measure in detail thepositions of many marks across the substrate area, if the apparatus isto print product features at the correct locations with very highaccuracy. The apparatus may be of a so-called dual stage type which hastwo substrate tables, each with a positioning system controlled by thecontrol unit LACU. While one substrate on one substrate table is beingexposed at the exposure station EXP, another substrate can be loadedonto the other substrate table at the measurement station MEA so thatvarious preparatory steps may be carried out. The measurement ofalignment marks is therefore very time-consuming and the provision oftwo substrate tables enables a substantial increase in the throughput ofthe apparatus. If the position sensor IF is not capable of measuring theposition of the substrate table while it is at the measurement stationas well as at the exposure station, a second position sensor may beprovided to enable the positions of the substrate table to be tracked atboth stations. Lithographic apparatus LA may for example is of aso-called dual stage type which has two substrate tables and twostations—an exposure station and a measurement station—between which thesubstrate tables can be exchanged.

Within the production facility, apparatus 100 forms part of a “lithocell” or “litho cluster” that contains also a coating apparatus 108 forapplying photosensitive resist and other coatings to substrates W forpatterning by the apparatus 100. At an output side of apparatus 100, abaking apparatus 110 and developing apparatus 112 are provided fordeveloping the exposed pattern into a physical resist pattern. Betweenall of these apparatuses, substrate handling systems take care ofsupporting the substrates and transferring them from one piece ofapparatus to the next. These apparatuses, which are often collectivelyreferred to as the track, are under the control of a track control unitwhich is itself controlled by a supervisory control system SCS, whichalso controls the lithographic apparatus via lithographic apparatuscontrol unit LACU. Thus, the different apparatus can be operated tomaximize throughput and processing efficiency. Supervisory controlsystem SCS receives recipe information R which provides in great detaila definition of the steps to be performed to create each patternedsubstrate.

Once the pattern has been applied and developed in the litho cell,patterned substrates 120 are transferred to other processing apparatusessuch as are illustrated at 122, 124, 126. A wide range of processingsteps is implemented by various apparatuses in a typical manufacturingfacility. For the sake of example, apparatus 122 in this embodiment isan etching station, and apparatus 124 performs a post-etch annealingstep. Further physical and/or chemical processing steps are applied infurther apparatuses, 126, etc. Numerous types of operation can berequired to make a real device, such as deposition of material,modification of surface material characteristics (oxidation, doping, ionimplantation etc.), chemical-mechanical polishing (CMP), and so forth.The apparatus 126 may, in practice, represent a series of differentprocessing steps performed in one or more apparatuses. As anotherexample, apparatus and processing steps may be provided for theimplementation of self-aligned multiple patterning, to produce multiplesmaller features based on a precursor pattern laid down by thelithographic apparatus.

As is well known, the manufacture of semiconductor devices involves manyrepetitions of such processing, to build up device structures withappropriate materials and patterns, layer-by-layer on the substrate.Accordingly, substrates 130 arriving at the litho cluster may be newlyprepared substrates, or they may be substrates that have been processedpreviously in this cluster or in another apparatus entirely. Similarly,depending on the required processing, substrates 132 on leavingapparatus 126 may be returned for a subsequent patterning operation inthe same litho cluster, they may be destined for patterning operationsin a different cluster, or they may be finished products to be sent fordicing and packaging.

Each layer of the product structure requires a different set of processsteps, and the apparatuses 126 used at each layer may be completelydifferent in type. Further, even where the processing steps to beapplied by the apparatus 126 are nominally the same, in a largefacility, there may be several supposedly identical machines working inparallel to perform the step 126 on different substrates. Smalldifferences in set-up or faults between these machines can mean thatthey influence different substrates in different ways. Even steps thatare relatively common to each layer, such as etching (apparatus 122) maybe implemented by several etching apparatuses that are nominallyidentical but working in parallel to maximize throughput. In practice,moreover, different layers require different etch processes, for examplechemical etches, plasma etches, according to the details of the materialto be etched, and special requirements such as, for example, anisotropicetching.

The previous and/or subsequent processes may be performed in otherlithography apparatuses, as just mentioned, and may even be performed indifferent types of lithography apparatus. For example, some layers inthe device manufacturing process which are very demanding in parameterssuch as resolution and overlay may be performed in a more advancedlithography tool than other layers that are less demanding. Thereforesome layers may be exposed in an immersion type lithography tool, whileothers are exposed in a ‘dry’ tool. Some layers may be exposed in a toolworking at DUV wavelengths, while others are exposed using EUVwavelength radiation.

In order that the substrates that are exposed by the lithographicapparatus are exposed correctly and consistently, it is desirable toinspect exposed substrates to measure properties such as overlay errorsbetween subsequent layers, line thicknesses, critical dimensions (CD),etc. Accordingly a manufacturing facility in which litho cell LC islocated also includes metrology system which receives some or all of thesubstrates W that have been processed in the litho cell. Metrologyresults are provided directly or indirectly to the supervisory controlsystem SCS. If errors are detected, adjustments may be made to exposuresof subsequent substrates, especially if the metrology can be done soonand fast enough that other substrates of the same batch are still to beexposed. Also, already exposed substrates may be stripped and reworkedto improve yield, or discarded, thereby avoiding performing furtherprocessing on substrates that are known to be faulty. In a case whereonly some target portions of a substrate are faulty, further exposurescan be performed only on those target portions which are good.

Also shown in FIG. 1 is a metrology apparatus 140 which is provided formaking measurements of parameters of the products at desired stages inthe manufacturing process. A common example of a metrology station in amodern lithographic production facility is a scatterometer, for examplea dark-field scatterometer, an angle-resolved scatterometer or aspectroscopic scatterometer, and it may be applied to measure propertiesof the developed substrates at 120 prior to etching in the apparatus122. Using metrology apparatus 140, it may be determined, for example,that important performance parameters such as overlay or criticaldimension (CD) do not meet specified accuracy requirements in thedeveloped resist. Prior to the etching step, the opportunity exists tostrip the developed resist and reprocess the substrates 120 through thelitho cluster. The metrology results 142 from the apparatus 140 can beused to maintain accurate performance of the patterning operations inthe litho cluster, by supervisory control system SCS and/or control unitLACU 106 making small adjustments over time, thereby minimizing the riskof products being made out-of-specification, and requiring re-work.

Additionally, metrology apparatus 140 and/or other metrology apparatuses(not shown) can be applied to measure properties of the processedsubstrates 132, 134, and incoming substrates 130. The metrologyapparatus can be used on the processed substrate to determine importantparameters such as overlay or CD.

During or before any actual imaging, the processing parameters may havea perturbation that causes them to deviate out of specification (e.g.,outside of the process window; i.e., a space of processing parametersunder which a pattern will be produced within specification) and thusmay lead to defects. For example, the focus may change due to topographyof a substrate to be exposed, drift in the substrate stage, deformationof the projection optics, etc.; the dose may change to due drift in thesource intensity, dwell time, etc. Various techniques may be used toidentify a processing parameter that is perturbed and to correct thatprocessing parameter. For example, if the focus is perturbed, e.g.,because an area of the substrate that is slightly raised from the restof the substrate is being exposed, the substrate stage may be moved ortilted to compensate for the perturbation.

Control of the lithographic process are typically based on measurementsfed back or fed forward and then modelled using, for example inter-field(across-substrate fingerprint) or intra-field (across-field fingerprint)models. Therefore modelling is typically limited to no better resolutionthan field fingerprint control, where a typical field may comprise 6 or8 dies, for example. At present, process control at a sub-die level(intra-die models) is not typically performed. Within a die, there maybe separate functional areas such as memory areas, logic areas, contactareas etc. Each different functional area, or different functional areatype may have a different process window, each with a differentprocesses window center. For example, different functional area typesmay have different heights, and therefore different best focus settings.Also, different functional area types may have different structurecomplexities and therefore different focus tolerances (focus processwindows) around each best focus. However, each of these differentfunctional areas will typically be formed using the same focus (or doseor position etc.) setting due to control grid resolution limitations.

The control of the lithographic apparatus may be achieved by modeling acorrection profile (e.g., a control profile) for the relevant parameter(or co-optimized for more than one parameter). The modelled correctionprofile for each parameter is fed into the lithographic apparatus, whichactuates the desired correction profile to control the lithographicprocess (exposure). The control may be based on feed forward models(e.g., from data measured within the lithographic apparatus prior toexposure). The scanner itself has self-correction which needs to beactuated during exposures by the scanner. These self-correctionscomprise, for example feed forward models such as reticle heating andwafer heating, machine calibrations such as wafer table shape and layoutdependent corrections.

Focus control is an example of a mainly feed forward control loop, basedon a large amount of levelling data collected for each substrate whichis used to determine corrections for exposure on that substrate whichcorrects for the surface topography. Other corrections are based onfeedback control loops. Focus control may, in addition to the main feedforward control just mentioned, also have a feedback element based onmeasurement of focus from exposed structures. Overlay control istypically based on a feedback loop; based on measurement of overlay fromprocessed substrates. Dose control has no feed forward control otherthan for mean dose, and is typically controlled in a feedback loop frompost exposure (e.g., after-etch) measurement, via a correction profiledetermined per field (e.g., separately in the scan and slit directions).

All these sources of corrections are input into the lithographicapparatus, which combines all of the corrections per exposure andactuates them, to optimize overlay, focus, dose and imaging performance.There are a number of methods for the lithographic process to actuatethe correction profile e.g., for control of focus/dose and/or overlay.An algorithm, essentially behaving as a filter, transforms thecorrections into setpoints for the stages and lens/mirrors. Thesetpoints are defined as time-dependent trajectories e.g., which definethe positioning and tilting of the reticle stage and/or wafer stagerelative to each other during exposure. By moving accordingly, theactuators dynamically control focusing and positioning of an image ofthe reticle onto the substrate. Such methods and others will be readilyapparent to the skilled person and will not be discussed further.

Controllability across the field is not constant and constraints oncontrollability may vary. For example, along the scan direction theremay be limits on the spatial scale of control (spatial frequencylimits). This causes an undesired variation in quality across thevarious dies (along the scan direction) within the field.

To address this, it is proposed to extend an exposure correction profile(e.g., for input to focus/dose or other actuators), for exposure of afield, beyond the regular (relevant) field dimension. As such thatcorrection profile may be modelled to include an area outside the field,so as to define additional setpoints beyond the start and/or end of theregular profile. More specifically the correction profile for each fieldmay be extended, so as to include control points (setpoints) immediatelybefore and after the field in the scan direction. This may be achievedby using relevant data from immediately outside the field (e.g., fromthe extended area). However, it may be preferred to determine additionalsetpoints outside the field area based on die layout information withinthe field. In an embodiment, this correction profile extension maycomprise appending one or more (average) die profiles outside the field,and as such can be based on knowledge of the (average) die profilewithin the field. The generated correction profile will result in areduction of intra-die variation in the correction quality (e.g., diesof interest effectively all become central dies).

In an embodiment, the method may comprise decomposing a measuredintra-field fingerprint into an intra-die and an “underlying intra-fieldfingerprint”; that is the intra-field fingerprint without the repeating(per die) intra-die component. It is then proposed that the intra-diefingerprints are corrected equally for all dies, including appended diesof an extended correction profile. A scaling factor fingerprint may beapplied to the intra die fingerprint, if appropriate; and possibly alsoto the intra reticle fingerprint (or possibly not, depending on theknown underlying physics, experimental data, or data analysis).

FIG. 2 illustrates this embodiment. The input is the raw (e.g.,measured) data 200. This may comprise any across-substrate data, such aslevelling data, overlay data, focus data, alignment data, dimensionaldata (e.g., critical dimension CD) etc., relevant for the correctionprofile to be determined. The raw data may comprise feed forward datafrom a substrate to be processed (e.g., as is typical for levelling dataor alignment data), or feedback data relating to one or more previouslyprocessed substrates (e.g., as is typical for overlay data, focus dataor CD data). At a first level, the raw data 200 is decomposed into anintra-field fingerprint 210 and inter-field fingerprint 220, wherein theintra-field fingerprint 210 is the component of the raw data which tendsto repeat per field. The exposure slit 225 and scanning direction SD isshown for reference. At a second level, the intra-field fingerprint 210is further decomposed into an intra-die fingerprint 230 and underlyingintra-field fingerprint 240. The intra-die fingerprint 230 is thecomponent of the intra-field fingerprint 240 which tends to repeat perdie. This step may comprise determining the intra-die fingerprint 230,and subtracting it from the intra-field fingerprint 210 to reveal theunderlying intra-field fingerprint 240.

At a final step, the correction profile for exposure of a fieldcomprising a plurality of dies is extended to correct for an area largerthan the field area. The correction profile may relate to (e.g.,correcting for) one or more of the inter-field fingerprint 220,intra-die fingerprint 230 and underlying intra-field fingerprint 240. Assuch, the correction profile may comprise a co-optimized correctionprofile which simultaneously corrects (as much as possible) for each ofthese fingerprints over the extended area. More specifically, thecorrection profile for correcting the intra-die fingerprint 230 may beextended over additional dies 250 (dotted border and no shading), beforeand after the within-field dies 260 (e.g., the dies within field area)in the scanning direction SD. The intra-die fingerprint attributed tothe additional dies 250 are assumed to be the same as determined for thefield dies 260 (as the intra-die fingerprint is assumed the same for alldies). The correction profile for correcting the underlying intra-fieldfingerprint 240 may be extended beyond the field area 260′ (e.g., via anextrapolation of the underlying intra-field fingerprint 240 data) toinclude correction for the same additional area 250′ relating toadditional dies 250. The correction profile which corrects theinter-field fingerprint 220 may be similarly extended to includecorrection for this additional area 250′, e.g., by fitting thecorrection profile to the inter-field fingerprint 220 data relating tothis area 250′.

In an embodiment, it is also proposed to enhance modeling of data forcontrol purposes by using the fact that the data exhibits a repeatingintra-die fingerprint 230. This knowledge can be used to effectivelyimpose constraints on the model, weighting for solutions which show asimilar tendency. Such a constraint can therefore be used to improvemodeling of the intra-die fingerprint and/or the inter-die fingerprintin either or both the scan direction and slit direction. In particular,this intra-die fingerprint may be used to improve intra-fieldfingerprint estimation in the slit direction. This may be particularlyuseful for dose control across the slit.

A further issue for such correction and control of a lithographicprocess is that of “fading” or lack of contrast. Fading is the effect ofthe finite size of the slit and the light intensity profile therein onimaging performance. For the actuation of the stages in the horizontalplane (i.e., relating to overlay) and/or the vertical plane (i.e.,relating to focus), present control algorithms translate the determinedcorrections into actuation setpoints; e.g., typically by minimizing RMS(root-mean-squared) residuals on the input corrections. Otheroptimization strategies may comprise maximizing the number of functionaldevices (dies-in-spec). The impact of fading is not considered duringthe optimization. This can have an impact on overlay and imaging for theexposed image.

Stage synchronization is characterized by Moving Standard Deviation(MSD) and Moving Average (MA) of the relative position of the substratestage, with respect to the reticle stage, over the time window in whicheach image point travels across the illumination slit width. Fading iscaused by a convolution of the determined high frequency correction(control profile) with the light intensity in the finite slit, resultingin an adverse MA and MSD impact. A typical current strategy forhorizontal stage actuation, for example, is to define a wafer stagetrajectory by a fitting algorithm which minimizes the RMS residuals onthe input fingerprint. The assumption behind this is that the slit isinfinitesimally small. As a result, no fading is considered, and theperformance on resist is a direct translation of the stage trajectoryresiduals (i.e., fit residuals). This assumption begins to fail in thepresence of high frequency trajectories and the resultant fading effectswill induce imaging penalties, through MSD. Moreover, the expectation onthe overlay or focus, i.e., the MA evaluation, shows significantdeterioration with respect to simple fitting residuals.

It is therefore proposed to address this issue by defining a strategyfor a balanced and optimal MA-MSD performance when actuating fingerprintthrough the scanner. The proposal comprises taking into account theknown finite slit width (the slit dimension in the scan direction) whendetermining the correction profile. This may comprise deconvolving theeffect of the slit width (e.g., the intensity profile within the slit)from the correction profile, using an appropriate scheme, to determine adeconvolved correction profile which provides improved performanceduring exposure. In a more specific embodiment, the method may compriseusing a Wiener Filter based algorithm to address the fading issue, whendetermining the correction profiles and defining scanner actuatorstrajectories. The proposed technique optimizes MA performance, overlayperformance, focus performance, and MSD performance, and thereforeimaging performance. The proposed technique can also be made flexible interms of MA versus MSD balance for specific applications.

One example of a high frequency intra-die fingerprint which may beencountered (e.g., in a 3DNAND production process) is that caused by amagnification in the scanning direction, per die. This fingerprintessentially forms a saw-tooth shape along the scanning direction, whichcan result in a saw-tooth overlay pattern, particularly without or withnon-ideal correction. FIG. 3 illustrates this issue. It comprises a plotof the dy (i.e., overlay) against the scanning direction Y. Each dot 300represents a (e.g., measured) data point. The fitted solid line 310 isthe correction profile to be actuated, which corresponds to theintra-die fingerprint as fitted to the data points (e.g., RMS-minimizedstage trajectory). The saw tooth pattern exhibited in the fingerprint isevident. The dotted line 320 is the predicted MA results as wouldactually be achieved using present methods, this representing aconvolution of the correction profile 310 with the slit intensityprofile.

FIG. 4 recasts the problem in mathematical terms, relating the fading tothe convolution with intensity profile within the slit. The problem isalso generalized for noise injected in the desired corrections; thereason for this will be described below. FIG. 4 shows that a presentconvolved noisy correction profile y comprises the input correctionprofile or setpoints s convolved 400 with slit intensity profile h toobtain noise-free convolved correction profile r which is subject to aninjection of noise n. Only the (noisy) convolved correction profile yand slit intensity profile h (i.e., the terms represented in boldface onthe Figure) are known. The aim is to deconvolve the slit profile 410 bydetermine a “deslitting” or deconvolution profile g which minimizes thedifference (e.g., minimizes the mean-squared error or RMS error) betweencorrected (or “deslitted”) correction profile or setpoints ŝ and inputcorrection profile s, given the slit intensity profile h and convolvednoisy correction profile y. Where the convolved noisy correction profiley is the available correction (as is the case here), then the problembecomes estimating the deslitted correction profiles ŝ that, ifactuated, would minimize the slit convolution error. In the presence ofnoise, the variables are random variable, and therefore the expectedvalue of deconvolution profile g may be taken to be:

g=argmin E(s−ŝ)²

In an embodiment, it is proposed to use a Weiner filter to solve thisproblem. The Wiener filter is a technique used in signal processing toextract a desired signal out of an observed noisy process. The Wienerfilter can be used, for instance, to recover an image which is blurredby a known low-pass filter. The Wiener filtering executes an optimaltrade-off between inverse filtering and noise smoothing.

FIG. 5 illustrates the Weiner filter solution. This solves the problemin the frequency domain by taking the Fourier transform or FFT of eachof the variables shown in FIG. 4 (in FIG. 5, uppercase variablesrepresent the transformed variables equivalent to those of FIG. 4). Thissimplifies the solution as the convolution now becomes a multiplication.The problem becomes:

G(f)=argmin E|S(f)=

|²

which can be solved by:

${G(f)} = \frac{{H^{*}(f)}{S_{PSD}(f)}}{{{{H(f)}}^{2}{S_{PSD}(f)}} + {N_{PSD}(f)}}$

where S_(PSD)(f) is the mean power spectral density of the originalcorrection profile s, N_(PSD)(f) is the mean power spectral density ofthe noise n and the superscript * denotes a complex conjugation.

In a further embodiment, the noise N_(PSD)(f) term may be used to tunethe optimization between MA and MSD. In an embodiment, the noise termN_(PSD) may be assumed to take a single value (white noise) over allfrequencies f. A lower value for the noise term N_(PSD) will enhance MAwhile degrading MSD, a higher value the do the opposite.

Several Noise levels can be studied by considering the PSD of thesignal. For the saw-tooth pattern being considered here, it has beenfound that a noise level of an order of magnitude of 10⁻¹⁹, and morespecifically (for example) of 7×10⁻¹⁹ may be optimal for best MAperformance; and a noise level of an order of magnitude of 10⁻¹⁷, andmore specifically (for example) of 4×10⁻¹⁷ may be optimal for best MSDperformance. These values have been considered for different amplitudesof the saw-tooth shapes, and for fingerprints comprising repetitions ofS-shapes, rather than the saw-tooth shape, and proved to be stable indelivering the best MA/MSD.

As such, a Wiener filter can be used to solve the problem illustrated byFIG. 4 and therefore provide deconvolved, corrected (deslitted)setpoints s for the actuators in the scanner. Referring back to FIG. 3,this will result in a much closer match for the convolved anddeconvolved correction profile (gray line) 330, determined using themethod described by FIG. 5, with the original correction profile to beactuated 310. This will be particularly the case when the noise term isoptimized for MA (e.g., optimized for best focus/overlay). Depending onthe application, the noise term could instead be optimized for MSD toimprove contrast and process latitude.

While this embodiment is described specifically in terms of overlaycaused by intra-die stress in the 3D-NAND process, it can be used tocorrect any other higher-order (e.g., overlay or focus) fingerprint inthe scan direction.

It should be noted that both of the main concepts (extension ofcorrection profile outside of the field area and deconvolution ordeslitting of the correction profile) can be combined. In fact, there issignificant benefit in combining the deconvolution embodiment with a(e.g., small) extension of the control signal, as any deconvolutionscheme is typically improved by provision of some setpoints outside theexposure field in order to generate more sensible results for theboundary points of the correction profile.

It should be further appreciated that the Wiener Filter baseddeconvolution scheme has far more extensive application than thelithography tools described herein. Such a concept can be extended toany imaging tools which uses a beam of photons or particles (for exampleelectrons) to print a desired image on a substrate (e.g., in resist/orto produce masks etc.).

In particular the use of a deconvolution scheme to improve a controlprofile of positioning of a beam of photons or particles with respect toa substrate may be adopted. Analog to a scanning exposure apparatushaving an illumination profile of finite length, also a beam of photonsor particles has a dimension which may be relatively large when comparedto the size of the functional devices that need to be applied to thesubstrate. The substrate in this example may be a reticle blank coatedwith a photoresist. The beam in this example will often be a beam ofelectrons as normally reticles (patterning devices) are patterned usingan e-beam writing tool. In addition to control of the beam position(typically with respect to coordinates within a plane of the substrate,being of importance of overlay error between layers on the substrate),control of the beam focus, beam intensity (dose) and beam extension(divergence and beam profile) may be pursued to optimize a quality ofthe functional devices, The quality of the beam control may be animportant property to assure properly manufactured functional devices ona patterning device or another substrate (wafer).

In an embodiment a method for controlling a scanning exposure apparatusconfigured for scanning a beam of photons or particles across asubstrate to form functional devices thereon is disclosed, the methodcomprising: determining a control profile for dynamic control of thebeam during scanning operation, wherein the beam is characterized by abeam profile comprising information of a spatial extension of the beamin at least a scanning direction; and optimizing a quality of beamcontrol by applying a deconvolution scheme to the control profile,wherein the structure of the deconvolution scheme is based on the beamprofile.

In another embodiment the control profile is for control of one or moreof: exposure dose (beam energy or intensity), focus of the beam,position of the beam in a plane of the substrate (overlay).

In another embodiment the control profile comprises a convoluted controlprofile which is convoluted with the beam profile, and saiddeconvolution scheme deconvolves the convoluted control profile tominimize an error resultant from the convolution.

In another embodiment the deconvolution scheme comprises determining aWeiner deconvolution filter which deconvolves the convoluted controlprofile and beam profile in the presence of noise.

In another embodiment a value for a noise term in said Weiner filter isselected to optimize a particular aspect of the beam control.

In another embodiment the selection of the value for the noise termcomprises tuning the balance between optimizing for moving average oroptimizing for moving standard deviation, describing positioningperformance of the beam relative to the substrate.

In further embodiments the control profile is determined by a computersystem taking into account that extension of the control profile beyondthe length of the exposure field is allowed and/or the control profileis determined taking a dimension of the illumination profile in thescanning direction into account. It is hence not essential to improve onan existing control profile by either extension and/or deconvolutionoperations, when generating a control profile the possibility ofextension and/or taking the finite dimension of the illumination profileinto account may be utilized to generate a control profile thatintrinsically provides a good quality of exposure for one or morefunctional areas comprised within the exposure field.

In an embodiment a control profile for dynamic control of theillumination profile is based on improving a quality of exposure of oneor more individual functional areas by: a) allowing the control profileto extend beyond the exposure field and/or b) taking the dimension ofthe illumination profile in the scanning direction into account.

In another embodiment the control profile defines setpoints over timefor one or more actuators which actuate the scanning exposure apparatus.

In another embodiment allowing the control profile to extend beyond theexposure field comprises determining setpoints for the actuators fortimes preceding and/or subsequent to an exposure time periodcorresponding to the exposure of the exposure field.

In another embodiment the control profile is allowed to extend beyondthe exposure field by an amount which is dependent on a dimension of thefunctional areas.

In another embodiment each functional area comprises a pattern which isrepeated over the field, and which corresponds to an individual die onthe exposed substrate, and said control profile is allowed to extend byat least one scan-in extension profile which precedes the exposure timeperiod and corresponds to an extended scan-in area, and at least onescan-out extension profile which follows the exposure time period andcorresponds to an extended scan-out area.

In another embodiment the control profile is for control of one or moreof: exposure dose, focus, overlay and leveling.

In another embodiment taking the dimension of the illumination profileinto account comprises convoluting the control profile with saidillumination profile as defined by an exposure slit and deconvolutingthe control profile using a deconvolution scheme to minimize an errorresultant from the convolution.

In another embodiment the deconvolution scheme comprises determining aWeiner deconvolution filter which deconvolves the convoluted controlprofile and illumination profile in the presence of noise.

In another embodiment selecting a value for the noise term in saidWeiner filter is used to improve the control profile.

In another embodiment a control recipe for the scanning exposureapparatus is generated based on the control profile.

Further embodiments of the inventions are disclosed in the list ofnumbered clauses below:

1. A method for controlling a scanning exposure apparatus configured forscanning an illumination profile over a substrate to form functionalareas thereon, the method comprising:

determining a control profile for dynamic control of the illuminationprofile during exposure of an exposure field comprising the functionalareas, in a scanning exposure operation; and

optimizing a quality of exposure of individual functional areas by:

a) extending the control profile beyond the extent of the exposure fieldin the scanning direction; and/or

b) applying a deconvolution scheme to the control profile, wherein thestructure of the deconvolution scheme is based on a dimension of theillumination profile in the scanning direction.

2. A method according to clause 1, wherein said control profile definessetpoints over time for one or more actuators which actuate the scanningexposure operation, and said step of extending the control profilecomprises determining setpoints for the actuators for times precedingand/or subsequent to an exposure time period corresponding to theexposure of the exposure field.3. A method according to clause 1 or 2, wherein said control profile isextended by appending an extension profile which is dependent on adimension of the functional areas.4. A method according to clause 3, wherein each functional areacomprises a pattern which is repeated over the field, and whichcorresponds to an individual die on the exposed substrate, and saidcontrol profile is extended by appending at least one scan-in extensionprofile which precedes the exposure time period and corresponds to anextended scan-in area, and at least one scan-out extension profile whichfollows the exposure time period and corresponds to an extended scan-outarea.5. A method according to clause 4, comprising the step of determining anaverage correction profile relating to each functional area and definingthe scan-in extension profile and scan-out extension profile as saidaverage correction profile.6. A method according to clause 5, wherein said average correctionprofile is determined based on an intra-die component of the controlprofile.7. A method according to clause 6, comprising decomposing the controlprofile into said intra-die component, an underlying intra-fieldcomponent and an inter-field component.8. A method according to clause 7, comprising extending the intra-diecomponent of the control signal by appending repetitions of theintra-die component over said extended scan-in area and said extendedscan-out area.9. A method according to clause 7 or 8, further comprising extending theunderlying intra-field component of the control signal by extrapolatingover said extended scan-in area and said extended scan-out area; and/orextending the inter-field component by fitting the inter-field componentdata relating to said extended scan-in area and said extended scan-outarea.10. A method according to any of clauses 6 to 9, comprising determininga constraint from said intra-die component in a modelling step to modelcontrol of the scanning exposure operation in one or both of the scandirection and slit direction, so as to determine the control profile.11. A method according to any preceding clause, wherein said controlprofile is for control of one or more of: exposure dose, focus, overlayand leveling.12. A method according to any preceding clause, wherein said controlprofile comprises a convoluted control profile which is convoluted withsaid illumination profile as defined by an exposure slit, and saiddeconvolution scheme deconvolves the convoluted control profile tominimize an error resultant from the convolution.13. A method according to clause 12, wherein said deconvolution schemecomprises determining a Weiner deconvolution filter which deconvolvesthe convoluted control profile and illumination profile in the presenceof noise.14. A method according to clause 13, comprising selecting a value forthe noise term in said Weiner filter to optimize a particular aspect ofcontrol.15. A method according to clause 14, wherein said selecting a value forthe noise term comprises tuning the balance between optimizing formoving average or optimizing for moving standard deviation, describingpositioning performance related to the relative positions of a substratestage for holding the substrate and a reticle stage for holding apatterning device.16. A method according to any preceding clause comprising performing oneor more subsequent exposure operations according to said controlprofile.17. A scanning exposure apparatus comprising a processor operable toperform the method of any of clauses 1 to 16.18. A scanning exposure apparatus according to clause 17, furthercomprising:an illumination source for providing exposure illumination;a reticle stage for holding a patterning device which patterns saidexposure illumination; anda substrate stage for holding the substrate.19. A computer program comprising program instructions operable toperform the method of any of clauses 1 to 16 when run on a suitableapparatus.20. A non-transient computer program carrier comprising the computerprogram of clause 19.21. A method for controlling a scanning exposure apparatus configuredfor scanning a beam of photons or particles across a substrate to formfunctional devices thereon, the method comprising:

obtaining a control profile for dynamic control of the beam duringscanning operation, wherein the beam is characterized by a beam profilecomprising information of a spatial extension of the beam in at least ascanning direction; and

optimizing a quality of beam control by applying a deconvolution schemeto the control profile, wherein the structure of the deconvolutionscheme is based on the beam profile.

22. A method according to clause 21, wherein said control profile is forcontrol of one or more of: exposure dose, focus, overlay and leveling.22. A method according to clause 21 or 22, wherein said control profilecomprises a convoluted control profile which is convoluted with the beamprofile, and said deconvolution scheme deconvolves the convolutedcontrol profile to minimize an error resultant from the convolution.23. A method according to clause 22, wherein said deconvolution schemecomprises determining a Weiner deconvolution filter which deconvolvesthe convoluted control profile and beam profile in the presence ofnoise.24. A method according to clause 23, comprising selecting a value forthe noise term in said Weiner filter to optimize a particular aspect ofthe beam control.25. A method according to clause 24, wherein said selecting a value forthe noise term comprises tuning the balance between optimizing formoving average or optimizing for moving standard deviation, describingpositioning performance related to the relative positions of a substratestage for holding the substrate and the beam.26. A method according to any of clauses 21 to 25, further comprisingperforming one or more subsequent scanning operations according to saidcontrol profile.27. An exposure apparatus comprising a processor operable to perform themethod of any of clauses 21 to 26.28. An exposure apparatus according to clause 27, further comprising:a source for providing the photons or particles; anda substrate stage for holding the substrate.29. A computer program comprising program instructions operable toperform the method of any of clauses 21 to 26 when run on a suitableapparatus.30. A non-transient computer program carrier comprising the computerprogram of clause 29.31. A method for controlling a scanning exposure apparatus configuredfor scanning an illumination profile over a substrate to form functionalareas thereon, the method comprising: obtaining a control profile fordynamic control of the illumination profile during exposure of anexposure field comprising the functional areas, in a scanning exposureoperation; and modifying the control profile to improve a quality ofexposure of one or more individual functional areas by: a) extending thecontrol profile beyond the extent of the exposure field in the scanningdirection and/or b) applying a deconvolution scheme to the controlprofile, wherein the structure of the deconvolution scheme is based on adimension of the illumination profile in the scanning direction.32. A method for determining a control profile for a scanning exposureapparatus configured to scan an illumination profile over a substrate toform an exposure field comprising functional areas thereon, the methodcomprising a step of determining a control profile for dynamic controlof the illumination profile based on improving a quality of exposure ofone or more individual functional areas by: a) allowing the controlprofile to extend beyond the exposure field and/or b) taking thedimension of the illumination profile in the scanning direction intoaccount.33. The method of clause 32, wherein said control profile definessetpoints over time for one or more actuators which actuate the scanningexposure apparatus.34. The method of clause 33, wherein allowing the control profile toextend beyond the exposure field comprises determining setpoints for theactuators for times preceding and/or subsequent to an exposure timeperiod corresponding to the exposure of the exposure field.35. The method of clause 34, wherein said control profile is allowed toextend beyond the exposure field by an amount which is dependent on adimension of the functional areas.36. The method of clause 35, wherein each functional area comprises apattern which is repeated over the field, and which corresponds to anindividual die on the exposed substrate, and said control profile isallowed to extend by at least one scan-in extension profile whichprecedes the exposure time period and corresponds to an extended scan-inarea, and at least one scan-out extension profile which follows theexposure time period and corresponds to an extended scan-out area.37. The method of clause 32, wherein said control profile is for controlof one or more of: exposure dose, focus, overlay and leveling.38. The method of clause 32, wherein said taking the dimension of theillumination profile into account comprises convoluting the controlprofile with said illumination profile as defined by an exposure slitand deconvoluting the control profile using a deconvolution scheme tominimize an error resultant from the convolution.39. The method of clause 38, wherein said deconvolution scheme comprisesdetermining a Weiner deconvolution filter which deconvolves theconvoluted control profile and illumination profile in the presence ofnoise.40. The method of clause 39, comprising selecting a value for the noiseterm in said Weiner filter to improve the control profile.41. The method of any of clauses 1-26 or 31-40, further comprisinggenerating a control recipe for the scanning exposure apparatus based onsaid control profile.

A class of control algorithms for a lithographic apparatus is so-calledDies In Specification (DIS) control. This method utilizes a controlstrategy which is targeted to obtain a maximum number of functioningdevices manufactured on a substrate. Typically this is achieved byutilizing a non-linear optimization method striving to limit the numberof occasions in which the maximum absolute value of a performanceparameter exceeds a critical threshold is minimized (also called “maxabs optimization).

A common objection against typical Dies In Specification (DIS) (max absoptimization based) control algorithms is that they would not be robust,because of sensitivity to outliers and reduced reliability whendepending on measurement data which is sparsely distributed across asubstrate (sparse sampling). A common way of dealing with outliers is touse an estimation model on measurement data (and an optimization modelafter that to create scanner setpoint profiles). The estimation model issupposed to filter outliers, and typically limits the data content to anexpected kind of shape (a model).

A modern scanning exposure apparatus allows dynamic control ofcorrection devices during the exposure of a die on a reticle. Hence witha certain resolution (depending on the involved actuator(s) and thedimension of the illumination profile in the scanning direction) acontrol profile for the correction devices may be dynamically adaptedalong the scanning direction. This allows dynamic optimization of acorrection profile defined across the slit direction during the scanningexposures of the die on the patterning device (reticle).

The here proposed control strategy modifies a static DIS based focus oroverlay control (for example leveling) algorithm. A static DIS controlmethod considers measurements associated with a die area and calculatesa control profile which is constant during the scanning exposure of thedie and maximizes the probability of the die being functional (e.g.yielding a functional device).

This static strategy is however not optimal as the dynamic adjustment ofthe control profile is not taken into account in case of pursuing a DIScontrol strategy. Hence a new control strategy is proposed targeted toachieve a maximum amount of yielding dies by splitting a (static) 2Doptimization into two 1D optimizations (separated into slit directionand scan direction). The key assumption of the algorithm is that forpractical cases the DIS optimization is limited by performanceparameters (typically related to yield of a process) variations acrossthe slit direction, meaning that the scan direction is of secondaryimportance. From that we first determine setpoints for the correctiondevices per position along the scan direction and then (low pass) filterthese setpoints to create an actuatable control profile. Actuatablerefers here to the achievable dynamical control of the control profileacross the scan direction (mainly limited by the finite dimension of theillumination profile in the scanning direction).

The slit direction DIS optimization is done first for a plurality ofpositions across the scanning direction. This involves determination ofa control profile based on a max abs optimization applied to performanceparameter data associated with an area oriented along the slit direction(X-axis), but limited to a certain range of Y-positions (Y-axis is herethe scanning direction). This determination of control profiles isrepeated for various Y-coordinates. The set of control profiles may befiltered to derive a dynamical control profile strategy which iscompatible with the correction capabilities of the lithographicapparatus (e.g. the resolution in the Y-direction of the correctionassociated with the control profile). Alternatively the chosen range ofthe Y-coordinates associated with the areas used to determine thecontrol profile may be chosen according to resolution limitations of thecorrections. Alternatively the control profile may be determined basedon performance parameter data associated with multiple areas, each arealocated at a different Y-coordinate. Additionally control profileparameters may be defined, determined as a function of the Y-coordinateusing a DIS based control algorithms and subsequently a fitting functionmay be used to describe the control profile as a function of theY-coordinate.

In an embodiment a method to control processing of substrates isdisclosed, the method comprising: a) obtaining values of a performanceparameter related to yield across a region of a substrate; b) dividingthe region into a plurality of sub-regions, each sub-region dimensionedin dependence of a spatial resolution of process control; and c)determining control profile settings based on non-linear modeling ofvalues of the performance parameter per individual sub-region or subsetof the plurality of sub-regions.

In an embodiment the method further comprises a step of filtering thecontrol profile settings based on the spatial resolution.

In an embodiment the method further comprises a step of fitting acontrol profile setting parameter to a function defined over the region.

In practice it is not always possible to achieve a 100% Dies inSpecification situation. It would be advantageous to release controlconstraints on certain dies across the wafer in order to guarantee thatenough control potential is available to still have an optimum amount ofyielding dies. The selection of the dies which are most limiting theprobabilities of having an acceptable number of dies meetingspecification needs to quantified in order to make this proposedstrategy viable.

In this document it is proposed to use Linear/Quadratic Programming(LP/QP) principles to select the dies which are most limiting the yield.

An objective function is defined mapping a control profile to anexpected performance parameter distribution. The control profile isoptimized to determine an optimal control profile across a field (e.g.performance parameter does not exceed critical limit at any positionwithin the field). The field in general comprises a plurality of dies(representing functional devices). To ensure each dies is yielding thecontrol profile settings are constrained to the requirement that theobjective function mapping the control profile also generatesperformance parameter data which is within specification for each die(100% yield). Additionally the control profile settings are constrainedto achievable control profile settings (based on characteristics of theactuators used for control for example).

As said, a solution “all dies in spec” does however not always exists,so some one or more dies then need to be sacrificed. A possibility is toremove dies from the constraints and verify which particular dieremoval(s) are optimal. Here it is proposed to consider the die specificconstraints as objective functions. The Lagrange multipliers associatedwith these objective functions are calculated. The dies for whichcontrol is most limited by the constraints have the largest number ofnon-zero valued Lagrange multipliers. These dies are removed first. Itis expected that in this way most control potential is released for theother dies.

In an embodiment a method to control a process is disclosed, the methodcomprising: a) obtaining values of a performance parameter related to ayield of the process across a region on a substrate subject to theprocess; b) dividing the region into a plurality of sub-regions; and c)determining a control setting for processing the region based on thevalues of the performance parameter and an expected yield of one or moresub-regions.

Although patterning devices in the form of a physical reticle have beendescribed, the term “patterning device” in this application alsoincludes a data product conveying a pattern in digital form, for exampleto be used in conjunction with a programmable patterning device.

Although specific reference may have been made above to the use ofembodiments of the invention in the context of optical lithography, itwill be appreciated that the invention may be used in otherapplications, for example imprint lithography, and where the contextallows, is not limited to optical lithography. In imprint lithography, atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

The terms “radiation” and “beam” used in relation to the lithographicapparatus encompass all types of electromagnetic radiation, includingultraviolet (UV) radiation (e.g., having a wavelength of or about 365,355, 248, 193, 157 or 126 nm) and extreme ultra-violet (EUV) radiation(e.g., having a wavelength in the range of 5-20 nm), as well as particlebeams, such as ion beams or electron beams.

The term “lens”, where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic and electrostaticoptical components.

The foregoing description of the specific embodiments will so fullyreveal the general nature of the invention that others can, by applyingknowledge within the skill of the art, readily modify and/or adapt forvarious applications such specific embodiments, without undueexperimentation, without departing from the general concept of thepresent invention. Therefore, such adaptations and modifications areintended to be within the meaning and range of equivalents of thedisclosed embodiments, based on the teaching and guidance presentedherein. It is to be understood that the phraseology or terminologyherein is for the purpose of description by example, and not oflimitation, such that the terminology or phraseology of the presentspecification is to be interpreted by the skilled artisan in light ofthe teachings and guidance.

The breadth and scope of the present invention should not be limited byany of the above-described exemplary embodiments, but should be definedonly in accordance with the following claims and their equivalents.

1. A method for controlling a scanning exposure apparatus configured forscanning an illumination profile over a substrate to form functionalareas thereon, the method comprising: obtaining a control profile fordynamic control of the illumination profile during scanning exposure ofan exposure field comprising the functional areas; and configuring, by ahardware computer system, the control profile to improve a quality ofexposure of one or more individual functional areas comprised within theexposure field by: a) extending the control profile beyond the extent ofthe exposure field in the scanning direction by appending an extensionprofile which is dependent on a dimension of one or more of thefunctional areas; and/or b) applying a deconvolution scheme to thecontrol profile, wherein the structure of the deconvolution scheme isbased on a dimension of the illumination profile in the scanningdirection.
 2. The method as claimed in claim 1, wherein the controlprofile defines setpoints over time for one or more actuators whichactuate the scanning exposure operation.
 3. The method as claimed inclaim 2, wherein the configuring of the control profile is implementedby extending the control profile and the extending the control profilecomprises determining setpoints for the one or more actuators for timespreceding, and/or subsequent to, an exposure time period correspondingto the exposure of the exposure field.
 4. (canceled)
 5. The method asclaimed in claim 1, wherein each functional area comprises a patternwhich is repeated over the field, and which corresponds to an individualdie on the exposed substrate, and the control profile is extended byappending at least one scan-in extension profile which precedes theexposure time period and corresponds to an extended scan-in area, and atleast one scan-out extension profile which follows the exposure timeperiod and corresponds to an extended scan-out area.
 6. The method asclaimed in claim 5, further comprising determining an average correctionprofile relating to each functional area and defining the scan-inextension profile and scan-out extension profile as the averagecorrection profile.
 7. The method as claimed in claim 6, wherein theaverage correction profile is determined based on an intra-die componentof the control profile.
 8. The method as claimed in claim 7, furthercomprising decomposing the control profile into the intra-die component,an underlying intra-field component and an inter-field component.
 9. Themethod as claimed in claim 1, wherein the control profile is for controlof one or more selected from: exposure dose, focus, overlay and/orleveling.
 10. The method as claimed in claim 1, wherein the controlprofile comprises a convoluted control profile which is convoluted withthe illumination profile as defined by an exposure slit, and thedeconvolution scheme deconvolves the convoluted control profile tominimize an error resultant from the convolution.
 11. The method asclaimed in claim 10, wherein the deconvolution scheme comprisesdetermining a Weiner deconvolution filter which deconvolves theconvoluted control profile and illumination profile in the presence ofnoise.
 12. The method as claimed in claim 10, further comprisingselecting a value for a noise term in the Weiner filter to improvecontrol of the scanning exposure apparatus.
 13. A scanning exposureapparatus comprising a processor configured to perform the method ofclaim
 1. 14. A computer program product comprising a non-transitorycomputer-readable medium comprising program instructions therein, theinstructions, upon execution by a computer apparatus, configured tocause the computer apparatus to at least perform the method of claim 1.15. A method for controlling a scanning apparatus configured forscanning a beam of photons or particles across a substrate to formfunctional devices thereon, the method comprising: obtaining a controlprofile for dynamic control of the beam during scanning operation,wherein the beam is characterized by a beam profile comprisinginformation of a spatial extension of the beam in at least a scanningdirection; and optimizing a quality of beam control by applying adeconvolution scheme to the control profile, wherein the structure ofthe deconvolution scheme is based on the beam profile.
 16. A method fordetermining a control profile for a scanning exposure apparatusconfigured to scan an illumination profile over a substrate to form anexposure field comprising functional areas thereon, the methodcomprising determining a control profile for dynamic control of theillumination profile based on improving a quality of exposure of one ormore individual functional areas by: a) allowing the control profile toextend beyond the exposure field and/or b) taking the dimension of theillumination profile in the scanning direction into account.
 17. Themethod as claimed in claim 16, wherein the control profile definessetpoints over time for one or more actuators which actuate the scan ofthe illumination profile.
 18. The method as claimed in claim 17, furthercomprising generating a control recipe for the scanning exposureapparatus based on the control profile.
 19. The method as claimed inclaim 17, wherein the determining a control profile comprising allowingthe control profile to extend beyond the exposure field and the allowingthe control profile to extend beyond the exposure field comprisesdetermining setpoints for the one or more actuators for times preceding,and/or subsequent to, an exposure time period corresponding to theexposure of the exposure field.
 20. The method as claimed in claim 16,wherein the determining a control profile comprising taking thedimension of the illumination profile into account and the taking thedimension of the illumination profile into account comprises convolutingthe control profile with the illumination profile as defined by anexposure slit and deconvoluting the control profile using adeconvolution scheme to minimize an error resultant from theconvolution.
 21. The method as claimed in claim 1, wherein theconfiguring of the control profile is implemented by applying thedeconvolution scheme and further comprising performing one or moresubsequent exposure operations according to the deconvolved controlprofile.